In order to keep light-emitting diode (LED) lights working in a stable state, a constant current source typically applied in LED drivers may meet two requirements: (i) its output current should be kept substantially constant; and (ii) power losses should be relatively low to obtain a relatively high system efficiency. In order to meet the first requirement, the output voltage of the constant current source may be kept higher than a threshold voltage for driving the constant current source steadily. Conventionally, the output voltage can be set according to a comparison of a sampling of an output voltage of the constant current source against a fixed reference voltage VREF.